Question

Question 1
Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).

Answer 1

To find the type of triangle, first we determine the length of all the three sides and see whatever condition of triangle is satisfied by these sides.
Now, using distance formula between two points,
$AB=\sqrt{(-4+5{)}^2+(-2-6{)}^2}=\sqrt{(1{)}^2+(-8{)}^2}=\sqrt{1+64}=\sqrt{65}\because d=\sqrt{(x_2-x_1)+(y_2-y_1{)}^2}BC=\sqrt{(7+4{)}^2+(5+2{)}^2}=\sqrt{(11{)}^2+(7{)}^2}=\sqrt{121+49}=\sqrt{170}AndCA=\sqrt{(-5-7{)}^2+(6-5{)}^2}=\sqrt{(-12{)}^2+(1{)}^2}\sqrt{144+1}=\sqrt{145}$
We see that, $AB\ne BC\ne CA$
And $\Delta ABC$ do not hold the condition of Pythagoras theorem
i.e., (Hypotenuse)${}^2$ = (Base)${}^2$ + (Perpendicular)${}^2$.
Hence, the required triangle is scalene because all sides are of different length.